When a sample is to be characterized for components, the components are generally separated from each other in a first step in order to identified and quantified in a later stage. However, it is not always possible to separate the components or it may not be motivated from a time/cost benefit reason. The samples may then be characterized spectroscopically whereby the components are identified by means of their unique spectral responses.
If one has a collection of samples and is aware of which components they comprise, it is, as a rule, trivial to determine their concentrations spectroscopically. This is due even if the spectral responses of the components overlaps each other. If, however, the components are unknown, the problem is muck more complicated. The situation was analysed for the first time in detail by the mathematics Lawton and Sylvestre (Technometrics, 13, 617, (1971)), who showed that it is impossible to find an unique solution even for a 2-component system. In 1990 we developed an experimental method, which partly solved this problem (Kubista, Chemometrics and Intelligent Laboratory Systems, 7, 273, (1990)). We then showed that if one carried out two spectroscopic measurements on each sample, in stead of one as previously used, and the measurements were such that the contribution of the components to these measurements had the same distribution of the intensities, but of different magnitude, then both the spectral responses as well as the concentrations of the components could be determined. Mathematically, these measurements are described using the equations:                     A        =                              C            ⁢                                                   ⁢            V            ⁢                                                   ⁢            or            ⁢                                                   ⁢                                          a                j                            ⁡                              (                λ                )                                              =                                    ∑                              i                =                1                            r                        ⁢                                          c                ij                            ⁢                                                v                  i                                ⁡                                  (                  λ                  )                                                                                                  j          =          1                ,                  2          ⁢                                           ⁢          …          ⁢                                           ⁢          n                                        B        =                              C            ⁢                                                   ⁢            D            ⁢                                                   ⁢            V            ⁢                                                   ⁢            or            ⁢                                                   ⁢                                          b                j                            ⁡                              (                λ                )                                              =                                    ∑                              i                =                1                            r                        ⁢                                          c                ij                            ⁢                              d                j                            ⁢                                                v                  i                                ⁡                                  (                  λ                  )                                                                                                  j          =          1                ,                  2          ⁢                                           ⁢          …          ⁢                                           ⁢          n                    wherein A is a matrix comprising spectra of the first type measured on the n samples; B is a matrix comprising spectra of the second type measured on the same n samples; C is a matrix comprising the concentrations of the r different components in the n samples; V is a matrix comprising the normalized spectra of the components; and D is a diagonal matrix, the r diagonal elements of which being the ratios between the responses of the components obtained in the two measurements. All spectra are digitalized in m points. We showed that the concentrations of the components (C), their normalized spectral responses (V) and the ratio between their responses obtained in the two measurements (D) could be determined only outgoing from the information obtained from the spectra as measured (A and B). We further described how the number of components of the samples (r) could be estimated.
One restriction using this method is that the number of components are not allowed to exceed the number of samples, which from a practical point of view means that the method can not be utilized on smaller series of samples and can not be applied on the whole for analysing isolated samples.
Several spectroscopic techniques, such as fluorescence, nmr, etc., can generate 2-dimensional data described by the equation:       I    ⁡          (              α        ,        β            )        =      κ    ⁢                   ⁢                  ∑                  i          =          1                r            ⁢                                    I            i                    ⁡                      (            α            )                          ⁢                  c          i                ⁢                              I            i                    ⁡                      (            β            )                              where the signal. I(α,β), is determined as a function of two variables, αand β, and are the sum of the contribution of the components in each point, which contribution is proportional to their concentrations (ci) and the products of their (normalized) 1-dimensional responses, Ii(α) and Ii(β). Out of these responses the components can be identified. In a steady state fluorescence spectroscopy Ii(α) and Ii(β) are the excitation- and emissions spectra of the components and are, as a rule, designated Iiex(λex) and Iicm(λcm), wherein λex and λcm are the excitation and emission wavelengths. The shape of an excitation spectra of a pure compound is, in general independent of the emission wavelength used at the measurement, and the corresponding is due for its emission spectrum. The fluorescence signal monitored, if necessary after a correction for the inner filter effect (Kubista et al, The Analyst, 119, 417 (1994)), is proportional to the concentration of the compound. In a sample containing more compounds the total signal is the sum of the contribution by each component. As fluorescence is measured in an arbitrary unit, eq. 1 contains a proportionally constant (κ).
The information of the 2-dimensional spectrum I(α,β) is insufficient to unambiguously determine the spectral responses of the components. Different approximative ways have been suggested but these do not function sufficient satisfactorily even for a 2-component mixture (Burdik and Tu, J. Chemometrics 3, 431, (1989)). 
The present invention is a method for analysing isolated test samples, or a couple of test samples without using references in such a way that the components can be identified.